2a^2-6a-3=0

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Solution for 2a^2-6a-3=0 equation:


Simplifying
2a2 + -6a + -3 = 0

Reorder the terms:
-3 + -6a + 2a2 = 0

Solving
-3 + -6a + 2a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1.5 + -3a + a2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -3a + 1.5 + a2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -3a + a2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -3a + a2 = 0 + 1.5
-3a + a2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-3a + a2 = 1.5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 1.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 1.5 + 2.25

Combine like terms: 1.5 + 2.25 = 3.75
2.25 + -3a + a2 = 3.75

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.936491673 and -1.936491673.

Subproblem 1

a + -1.5 = 1.936491673 Simplifying a + -1.5 = 1.936491673 Reorder the terms: -1.5 + a = 1.936491673 Solving -1.5 + a = 1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = 1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = 1.936491673 + 1.5 a = 1.936491673 + 1.5 Combine like terms: 1.936491673 + 1.5 = 3.436491673 a = 3.436491673 Simplifying a = 3.436491673

Subproblem 2

a + -1.5 = -1.936491673 Simplifying a + -1.5 = -1.936491673 Reorder the terms: -1.5 + a = -1.936491673 Solving -1.5 + a = -1.936491673 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + a = -1.936491673 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + a = -1.936491673 + 1.5 a = -1.936491673 + 1.5 Combine like terms: -1.936491673 + 1.5 = -0.436491673 a = -0.436491673 Simplifying a = -0.436491673

Solution

The solution to the problem is based on the solutions from the subproblems. a = {3.436491673, -0.436491673}

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